When you build relationship with Cait and eventually she wants to get clean, does she have to get clean or can you talk her out of it, keep her a junkie and still romance her?

I think she has to get clean. I think completement of her quest is necessary in order to max out her affinity.

Yes. She is my companion and you do have to finish it, then your reward for the effort happens a little while later. In my case it wasn't at the best time, but was welcome none the less..